General Relativity and Quantum Cosmology

Title:Singularity-free Bianchi spaces with nonlinear electrodynamics

Abstract: In this paper we present an analysis to determine the existence of
singularities in spatially homogeneous anisotropic universes filled with
nonlinear electromagnetic radiation. These spaces are conformal to Bianchi
spaces admitting a three parameter group of motions G$_3$. For these models we
study geodesic completeness. It is shown that with nonlinear electromagnetic
field some of the Bianchi spaces are geodesically complete, like G$_3$IX and
G$_3$VIII; however, completeness depends on the curvature of the space. When
certain topology is assumed, Bianchi G$_3$IX presents geodesics that are
imprisoned. It is surprising that in the linear limit (Maxwell field) the
spacetimes are singularity-free even if the curvature parameter is zero.